(Too long for a comment, hence posted as an answer.)
On what basis do you rest the claim that "Professor Snape specifically wanted to keep [his love for Harry's mother] a secret"? As far as I can tell, (a) Snape's love for Lily was never a secret and (b) at no point did Snape make Harry promise to keep this (non-)secret.
When Snape, Lily Evans, James Potter, Sirius Black, Remus Lupin etc attended Hogwarts, it was widely known that Snape admired and loved Lily. Voldemort too knew that Snape had been in love with Lily. Not much of a secret, this piece of knowledge... It is probably true that not many people knew the reason for why Snape's Patronus was a doe -- that Lily's Patronus was a doe too. However, that's just one -- admittedly very tangible -- proof of the strong feelings Snape felt for Lily, not a revelation of the underlying secret.
For sure, Snape made Dumbledore promise -- immediately following the deaths of Harry's parents -- that he (Dumbledore) would never let Harry know that Snape was committed to helping Harry survive and succeed. Importantly, though, Snape extracted no such promise before giving Harry his memories as he was dying from Nagini's bites. Harry was thus free to make use of the memories as he saw fit.
The two preceding paragraphs are based on the very end of Chapter 32, "The Elder Wand", and on Chapter 33, "The Prince's Tale", in HP7.